Due 1/15: Prove the Corollary stated in class.
Due 1/23: Prove that the existence of inverse in the
definition of the formal groups can be deduced from the other
axioms. Prove that the map defined
in the class O_K \to End(F_f) is a homomorphism. Given two
elements f and g in F_\varpi, apart from [1]_{g, f}, can you find
some other isomorphisms between them?
Due 1/30: Prove that if a \in Z_p, m \in Z, then (a
choose m) \in Z_p. Prove the proposition on Newton polygon.
Use it to prove the characterization of the totally ramified
extension.